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A von
B Bauhaus-University Weimar, Germany
W und
Chair of Mineral Processing of
Building Materials and Reuse
PARTICLE SIZE AND SHAPE –
IMPORTANT FACTORS FOR
PACKING DENSITY
Dr.- Ing. Ursula Stark
Prof. Dr.- Ing. habil. Anette Mueller
Bauhaus-University Weimar Germany
1
A B Bauhaus-University Weimar
TOPICS
von
W und
Chair of Mineral Processing of Building
Materials and Reuse
1. Definitions of particle size and shape and
bulk density
2. Packing density - state of the art
3. Measuring methods
4. Results
2
A B Bauhaus-University Weimar
1. Definitions
von
W und
Chair of Mineral Processing of Building
Materials and Reuse
Particle size
A non spherical particle has many dimensions. Which
dimension is measured as particle size depends on:
• the measuring method
• the characteristic particle feature and
• the particle morphology
Each measuring method has an own definition!
Basically the particle size is defined as the equivalent
diameter of a ball, which has the same measuring effekt like
the real particle.
3
A B Bauhaus-University Weimar
1. Definitions
von
W und
Chair of Mineral Processing of Building
Materials and Reuse
Particle shape
Fundamental definitions:
- Ratio of particle length to particle width and
the resultant fraction
L
W
- Sphericity as ratio of measured circumference of
particle projection and the circumference of a circle
of the same area
U
SPHT =
2⋅ π⋅ A
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A B Bauhaus-University Weimar
1. Definitions
von
W und
Chair of Mineral Processing of Building
Materials and Reuse
Packing density
• Total volume Vt =
solid volume Vs + void volume Vv
• Void porosity ε = Vv / Vt
• Packing density Φ = Vs / Vt
• Unit mass ρum = Φ· ρparticle bulk density
Conditions of measurement influence void porosity and
packing density!
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A B Bauhaus-University Weimar
1. Definitions
von
W und
Chair of Mineral Processing of Building
Materials and Reuse
Packing density - conditions of measurement
Loose packing density:
The granular material is filled in a
defined volume without any
compaction.
Tap density:
The granular material is compacted
by shocks.
Vibrating density:
The granular material is compacted
by vibration.
6
A B Bauhaus-University Weimar
2. Packing Density
von
W und
Chair of Mineral Processing of Building
Materials and Reuse
Early works about packing density
Experimental and theoretical approaches to find grading
curves of aggregates with a minimum of voids
Fuller and Grading curve with a minimum of voids
1907
Thomson determinated by experimental work
Packing theory for sphere shaped
Furnas 1931
particles
Andreasen
1930 Packing density of ceramic materials
and Andersen
Packing density in geotechnical appli-
Manegold 1955
cations
7
A B Bauhaus-University Weimar
2. Packing Density
von
W und
Chair of Mineral Processing of Building
Materials and Reuse
Early works about packing density
Experimental and theoretical approaches to find grading
curves of aggregates with a minimum of voids
Fuller and Grading curve with a minimum of voids
1907 Q = (x/xmax)m; m = 0,5
Thomson determinated by experimental work
Base of model: Small particles fill out the
Packing theory for sphere shaped
Furnas 1931 cavities between the big particles without
particles
disturbing the packing of the big particles.
Andreasen
1930 Packing density of ceramic materials
and Andersen
Packing density in geotechnical appli-
Manegold 1955
cations
8
A B Bauhaus-University Weimar
2. Packing Density
von
W und
Chair of Mineral Processing of Building
Materials and Reuse
Works in the „pre computer“ age
• Broadening and deepening of the earlier approaches
• Development of models for random packing of spheres
• Empirical consideration of influence of shape
Experimental determination of void
Hummel 1959 porosity of aggregates. Parameters:
Fuller exponent and the particle shape.
Calculation scheme on basis of void
porosity of single sized spheres consi-
Schwanda 1959 dering interactions between particles.
Parameters: Fuller exponent and empi-
rically characterized particle shape.
9
A B Bauhaus-University Weimar
2. Packing Density
von
W und
Chair of Mineral Processing of Building
Materials and Reuse
Works in the „pre computer“ age
Empirical equation of void porosity as
Peronius and function of Fuller exponent, particle
1985
Sweeting shape and compaction. Shape charac-
terized by Powers’ scale of roundness.
Empirical equation of void porosity of
any particle size distribution as function
Aberg 1992
of particle shape. Shape characterized
empirically.
Theoretical model of void porosity for
Yu, Standish, 1993 continuous or mixed single-sized
and Zou 1997 distributions of different shape.
Experimental calibration necessary.
Empirical equation of void porosity of
Tsirel 1997 particle size distributions acc. to Fuller
as function of particle shape. 10
A B Bauhaus-University Weimar
2. Packing Density
von
W und
Chair of Mineral Processing of Building
Materials and Reuse
Works in the „computer“ age
• Numerical modeling of packing density of spheres
• First analytical consideration of influence of shape
Model on basis of packing of binary
Stovall et al., 1986 mixtures, extended to multi-sized
Glavind et al. 1999 mixtures. Inclusion of experimen-
tally determined packing densities.
Packing model of multi-sized granu-
lar materials considering interactions
De Larrard 1999 between the particles and wall
effects. Experimentally determined
parameters included.
11
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2. Packing Density
von
W und
Chair of Mineral Processing of Building
Materials and Reuse
Works in the „computer“ age
DEM-simulation of dense random
Stroeven
1999 packs of spheres with different size
and Stroeven
distributions.
Spatial-statistical analyses
Stoyan et al. 2001 for simulated random packings of
spheres with random diameters
Space filling tetrahedron assembly
Latham et al. 2001 model and dynamic interaction model
for real-shaped particles.
12
A B Bauhaus-University Weimar
2. Packing Density
von
W und
Chair of Mineral Processing of Building
Materials and Reuse
Comparison of “gravel” and “crushed aggregates”
acc. to different measurements and models:
∆ = 100 · (εgravel – εcrushed aggregates)/ εcrushed aggregates
ε ∆
“crushed
“gravel” Compared at
Aggr.”
Hummel 0,188 0,235 22 % ε = min
Schwanda 0,132 0,244 46 % ε = min
Peronius 0,130 0,235 45 % m = 0,5 = const
Tsirel 0,176 0,217 19 % m = 0,5 = const
Latham 0,374 0,568 34 % ε = min
13
A B Bauhaus-University Weimar
3. Methods
von
W und
Chair of Mineral Processing of Building
Materials and Reuse
Sieving method
w
Geometrical comparison Particle size = equivalent
between particle size ball diameter with size of
and sieve aperture mesh w
14
A B Bauhaus-University Weimar
3. Methods
von
W und
Chair of Mineral Processing of Building
Materials and Reuse
Particle shape with gauge method –
Shape Index SI
Measurement based on the funda-mental SI = (M2/M1) 100
definition:
ratio Length to Width
1. Ratio of sizes of gauge: Length / Width = 3/1
2. Separating of all grains with L / W > 3
3. Weighing:
M1 - Mass of complete sample / Gramm
M2 - Mass of non-cuboid grains / Gramm
Amount of total sample:
Minimum 300 Grains per fraktion
15
A B Bauhaus-University Weimar
3. Methods
von
W und
Chair of Mineral Processing of Building
Materials and Reuse
Particle size and shape with photo-optical method
PC: controlling
Dosing of sample and calculating
sofware
Light
Camera
source
2 1
Schematic structure of a photo-optical particle size and
shape analyser.
The used device: HAVER CPA 4-2 real time
16
A B Bauhaus-University Weimar
3. Methods
von
W und
Chair of Mineral Processing of Building
Materials and Reuse
Particle size and shape dimensions
Shadow projection Image analyses
Circumference U
L
Area A of projection
B
Largest Length
Measuring direction
Largest Width
Particle size = Diameter of
D circle with the same area like
the projection area A
17
A B Bauhaus-University Weimar
4. Results
von
W und
Chair of Mineral Processing of Building
Materials and Reuse
Comparison particle size distributions:
sieve and CPA analyses
100 100
Sieve Sieve
80 80
Passage / %
Passage / %
CPA CPA
60 60
40 40
20 20
0 0
0,1 1 10 100 0,1 1 10 100
Particle size / mm Particle size / mm
Cuboid particles Gritty to flaky particles
18
A B Bauhaus-University Weimar
4. Results
von
W und
Chair of Mineral Processing of Building
Materials and Reuse
Comparison particle shape results:
gauge and CPA analyses
2
L / W - CPA
1,8
1,6 y=x
1,4
1,2
1,2 1,4 1,6 1,8 2
L / W - Gauge
In both cases mean sizes of L/W- Para-
meters based on number distribution
19
A B Bauhaus-University Weimar
5. Results
von
W und
Chair of Mineral Processing of Building
Materials and Reuse
Correlation - shape parameters L / W and SI
100
Analysed both
natural and crushed
Shape Index SI [%]
80
aggregate fractions and
60
also modelling fractions
40
by shape
L / W – mean:
20
calculation based on
0 volume distribution
1 1,2 1,4 1,6 1,8 2 2,2 2,4
L / W, CPA [-]
20
A B Bauhaus-University Weimar
5. Results
von
W und
Chair of Mineral Processing of Building
Materials and Reuse
Tap density in comparison with particle shape
1,8
SPHT Analysed
1,6
Tap Density
L/W fractions
[kg/dm³]
1,4 with different
shape and
1,2 size:
8/16 mm
1 16/32 mm
1 1,2 1,4 1,6 1,8 2
8/32 mm.
SPHT, L / W [-]
21
A B Bauhaus-University Weimar
5. Results
von
W und
Chair of Mineral Processing of Building
Materials and Reuse
Influence of particle shape on packing density
0,80 Gabbro
0,75
Packing density [-]
Quarzit
0,70
0,65 Granodiorid
0,60
Kalkstein
0,55
0,50
Marmor
1,00 1,05 1,10 1,15 1,20 1,25
Sphericity SPHT [-]
Rheinkies
Authors: Graubner / Proske / Ramge, TU Darmstadt
22
A B Bauhaus-University Weimar
5. Results
von
W und
Chair of Mineral Processing of Building
Materials and Reuse
Influence of particle shape on packing density
0,80
1 Gabbro
Darmstadt:
0,75
Packing density [-] [-]
Darmstadt Gabbro
Quarzit
Packing density
0,8
0,70
Weimar Quarzit
0,65 Granodiorid
0,6 Granodiorit
0,60
Kalkstein
Kalkstein
0,55
0,4 Marmor
0,50
Marmor
1,00 1,05 1,10 1,15 1,20 1,25Rheinkies
0,2
Sphericity SPHT [-] Weimar:
1 1,1 1,2 1,3 1,4 Rheinkies
Authors: Graubner / Proske / Ramge, TU Darmstadt
Sphericity [-] Kalkstein
23
A B Bauhaus-University Weimar
CONCLUSIONS
von
W und
Chair of Mineral Processing of Building
Materials and Reuse
Simulation models:
Mostly balls are considered. Large differences between
the results are obtained.
New photo-optical measuring methods:
Particle size and particle shape can be determined
quantitatively.
Influence of particle shape:
First measuring results of relationship between
SI-Index and photo-optical measured L / W ratio
Packing density and L / W ratio and SPHT
24
A B Bauhaus-University Weimar
OUTLOOK
von
W und
Chair of Mineral Processing of Building
Materials and Reuse
Future works:
Investigations and experiments about the influence of
particle shape on all relevant properties of bulk materials.
25
A B Bauhaus-University Weimar
LITERATURE (1)
von
W und
Chair of Mineral Processing of Building
Materials and Reuse
Aberg, B. Void ratio of non-cohesive soils and similar materials.
J. Geotech. Eng. 118 (9) (1992) 1315 – 1334.
Bezrukov, A., Stoyan, D. Spatial statistics for simulated packings of spheres.
Bargiel, M. Image Anal Stereol 2001;20:203-206.
Fuller, W.B., Thomson, S.E. The Laws of Proportioning Concrete.
Transactions of the American Society of Civil Engineers, Vol.
LIX, New York, Dec. 1907.
Furnas, C. C. Grading Aggregates.
Industrieal and Engineering Chemistry, American Chemiscal
Society (ACE), Vol. 23, No. 9, Easton, Pa., 1931.
Glavind, M., Pedersen, E.J. Packing calculations applied for concrete mix design.
Proceedings Creating with Concrete, May 1999, University of
Dundee.
Glavind, M., Stang, H.A. A geometrical packing model as a basis for composing
cement paste containing clay for high strength concrete.
Proceedings from the Third Int.
Symposium on Brittle Matrix Composites BMC3 (ed.
A.M.Brandt and I.H. Marshall) 1992, pp. 508-518.
Hummel, A. Das Beton-ABC.
12. Aufl., Verlag Ernst und Sohn, Berlin, 1959. 26
A B Bauhaus-University Weimar
LITERATURE (2)
von
W und
Chair of Mineral Processing of Building
Materials and Reuse
Latham, J., Munjiza, A., On the prediction of void porosity and packing of rock particulates.
Lu, Y. Powder Technologie (2002) 1, 10 – 27.
Manegold, E. Kapillarsysteme. Band 1, Grundlagen, Straßenbau, Chemie und
Technik Verlagsgesellschaft, Heidelberg, 1955.
Peronius, N., Sweeting, T.J. On the correlation of minimum porosity with particle size distribution.
Powder Technologie 42 (1985) 113 – 121.
Schwanda, F. Der Hohlraumgehalt von Korngemischen.
Beton 9 (1959)1, 12 – 17, 427 – 431.
Stovall, T., De, Larrard, F., Linear packing density model of grain mixtures.
Buil, M. Powder Technology 48 (1986), 1 – 12.
Stroeven, P., Stroeven, M. Assessment of packing characteristics by computer simulation.
Cement and Concrete Research 29 (1999) 1201-1206.
Tsirel, S.V. Methods of granular and fragmented material packing density
calculation.
Int. J. Rock Mech. Min. Sci. 34 (2) , 1997, 263 – 273.
Yu, A.B., Standish, N. A study of the packing of particles with mixture size distribution.
Powder Technologie 76 (1993) 113 – 124.
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